Problem: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BCA$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle ECF \cong \angle ACB$ $, \ $ $ \angle CEF \cong \angle BAC$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \overline{BD} \cong \overline{BC}$ $, \ $ and $\ $ $ \angle BDE \cong \angle ACB$ Proof $ \triangle BCA \cong \triangle BDE$ because ASA $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle FCE$ because AAS $ \overline{AC} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BCE$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.